An Algorithm is a finite list of clear instructions used to solve a problem.

The bloch sphere is a model used to represent the state of one qubit as a point on the surface of a sphere.

Complexity classes are classes of problems that require similar resources like runtime.

Entanglement is a phenomenon of quantum physics that is used in quantum computing. Two qubits can be entangled with each other. If we then measure the state of one of the qubits, you automatically know the state of the other qubit.

Gates are the building blocks of quantum algorithms. They are the logical representation of operations we can perform on qubits.
To learn more about all the different gates, take a look at our cheat sheet for circuit magicians.

Ket notation makes use of vertical bars \(|\) and angle brackets \(\rangle \) to denote quantum states like \(\ket{0}\). Mathematically, a "ket" can be considered a vector.
Two superpositional states have special symbols assigned to them in ket notation. They are obtained by applying a Hadamard gate H to \(\ket{0}\) and \(\ket{1}\):

• \(H\ket{0} = \ket{+} = \frac{1}{\sqrt{2}}(\ket{0} + \ket{1}) \)
• \( H \ket{1}= \ket{-} = \frac{1}{\sqrt{2}}(\ket{0} - \ket{1}) \)

Optimization problems such as finding the best routes for a fleet of logistic trucks require huge resources for classical computations and are on the anticipated applications for quantum computing.

Phase is a property of quantum states and not discovered in measurements. However phase differences can be turned into measurable (amplitude) differences. For a single qubit, the phase can be thought of as the rotation angle around the north-south pole axis of the bloch sphere.

Runtime complexity of an algorithm describes how the execution time changes with the size of the input data.

Simulation of quantum systems is about simulating the behavior of things like molecules to learn more about their structure, properties, or behavior. This is very hard to do on a classical computer, thus an interesting use case for quantum computing.

A qubit can be in state \(\ket{0}\), in state \(\ket{1}\), or be in something called a superposition of \(\ket{0}\) and \(\ket{1}\). Then it has a certain probability to be measured as \(\ket{0}\) or \(\ket{1}\). However, a measurement destroys the superposition – i.e. all the subsequent measurements will give you the same result that you have obtained in the first place.

Machine learning describes a sub-field of artificial intelligence where the computer learns from data provided. It is another anticipated use case for quantum computing.